An oscillator is a widely used electronic circuit component that generates a periodic output voltage signal at a particular frequency. An oscillator is an autonomous circuit in the sense that the oscillator can generate a periodic output voltage signal by applying only constant bias signals to the oscillator, through a self-sustaining mechanism that causes repeated amplification of the oscillator's own noise that eventually becomes a large periodic voltage signal. When the amplitude of the oscillation reaches a predetermined level, another different mechanism of the oscillator limits further growth of the signal so that the amplitude of the oscillation maintains the predetermined level. The amplitude and frequency of the oscillation is usually determined by the properties of the oscillator and its surrounding circuitry.
Oscillators are extensively used in a variety of electronic circuits including microprocessors, digital signal processors, frequency synthesizers, and analog circuits with phase-locked loops (PLLs). In microprocessors and other digital system-on-chip (SOC) applications, oscillators are used for clock generation. In communication systems such as wireless local area networks (WLAN) and cellular telephone transceivers, oscillators are used for frequency translation of the information signal and for channel selection.
For a variety of applications, it is desirable to have a mechanism to adjust the frequency or period of oscillation of an oscillator. For example, if an oscillator is used to select a channel during the down conversion of a signal in a radio frequency (RF) transceiver, there is a need for the oscillator to operate at different frequencies at different times. If the output frequency of an oscillator can be varied by a control voltage of the oscillator, the oscillator is called a voltage controlled oscillator (VCO). On the other hand, if the output frequency of the oscillator can be controlled by varying a control current of the oscillator, the oscillator is called a current controlled oscillator. The term VCO herein can be applied to both the voltage controlled oscillator and the current controlled oscillator.
VCOs are commonly used in phase-locked loop circuits, which are also widely used in analog circuits such as wireless communication systems. FIG. 1 is a block diagram illustrating a typical phase-locked loop (PLL) 100 including a VCO 112. The PLL 100 includes an oscillator-frequency divider (OSC+FD) module 102, a phase detector (PD) module 108 comprised of a phase frequency detector (PFD) 104 and a charge pump (CP) 106, a low-pass filter (LF) 110, a VCO 112, and a frequency divider (FD) 114. The oscillator-frequency divider (OSC+FD) module 102 generates a reference signal (REF) 116. The phase detector (PD) 108 compares the phase of the reference signal (REF) 116 with the phase of a feedback signal (FB) 118. The difference in the phases of the reference signal (REF) 116 and the feedback signal (FB) 118 is filtered by a low-pass filter (LF) 110, and the filtered phase difference signal 122 is applied to the controlling node of the VCO 112. The VCO 112 outputs a signal 128 at a locked frequency determined by the voltage of the filtered phase difference signal 122 at the controlling node of the VCO 112. Therefore, in analyzing PLLs, it is important to determine the behavior of the VCO 112, including the control voltage of the VCO 112.
Because oscillators are commonly used in electronic circuits, the analysis of the operation of oscillators is also important in understanding and simulating the behavior of a given electronic circuit. Specifically, the steady state analysis of electronic circuits and oscillators is of interest in circuit simulation. In circuit simulation, a circuit is typically characterized using a set of differential algebraic equations (DAEs). The steady state solution of a DAE is the asymptotic solution of the system as the effect of an initial condition dies out.
There are different types of steady state behaviors that are of interest in analyzing a circuit. One of such steady state behaviors is the DC operating point of the circuit, which provides the voltages and currents at various circuit nodes when the circuit is driven by time-dependent constant excitations. This DC operating point of the circuit can be analyzed using conventional circuit simulation software such as SPICE.
Another type of steady state behavior, the periodic steady state (PSS),is obtained when a circuit is driven by a set of periodic excitations. Since the circuit is driven by an external input and is not autonomous, the circuit steady state is response is also periodic with the same period as the period of the external input signal. However, oscillators achieve a periodic steady state when driven by constant excitations. Therefore, in the case of oscillators, as part of analyzing the steady state, the period of frequency of oscillation also needs to be calculated together with the voltages and currents associated with the oscillators.
A variety of conventional techniques exist for computing the steady state behavior of a VCO. However, all of these conventional techniques determine the steady state behavior of a VCO where the control voltage of the VCO is given (known) and the period of frequency of oscillation is unknown. In other words, it is assumed that the control voltage of the VCO is known and that the frequency of oscillators as well as the voltages at various nodes of the VCO needs to be computer for this given value of the control voltage.
For example, a well-known but error-prone conventional technique of determining the period of oscillation of a VCO is to run a dynamic transient simulation of the VCO circuit. If this simulation is run for a sufficiently long duration, the VCO circuit reaches its steady state. The period of oscillation can be estimated by measuring the difference in times when the output signal waveform of the VCO crosses a predetermined constant value for two consecutive times. However, this conventional technique is error prone, because it is difficult to verify whether the circuit has indeed reached a steady state for all the nodes in the VCO circuit.
Another conventional technique of determining the period of oscillation of a VCO is to computer the steady state by treating the period to be an unknown and computing this period together with all the node voltage/current waveforms of the circuit. Such conventional technique can be applied in both time domain and frequency domain. In time-domain, a widely used method is the Shooting-Newton method and in frequency-domain a widely used method is the Harmonic Balance method. However, this conventional technique also assumes that the control voltage of the VCO is known, and the period of frequency of oscillation is calculated as part of the algorithm.
So far, there has been non conventional technique of determining the control voltage of a VCO given a known period or frequency of oscillation of the VCO. One rudimentary way of determining the control voltage of a VCO given a known period or frequency of oscillation of the VCO is to calculate the control voltage for a given period using an iterative technique where the control voltage is assumed to be a certain value and the corresponding frequency or period of oscillation is computed. If the assumed value of the control voltage is swept in sufficiently small increments, in theory one can find the correct control voltage that leads to the given frequency of oscillation. However, this iterative technique is very inefficient, since it requires multiple, iteratively steady state computations of the VCO circuit to determine the correct control voltage.
Therefore, there is a need for determining the control voltage of a VCO given the frequency or period of oscillation of the VCO as part of the computation of the steady state solution of the VCO with the control voltage being an unknown variable. There is also a need for determining the control voltage of a VCO given the frequency or period of oscillation of the VCO in an efficient manner.